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Sound power level estimation - choice of the prior distribution

Stępień Bartłomiej

Vibrations in Physical Systems

2023

Vol. 34, nr 1

art. no. 2023110

Bayesian inference is one of the methods used to determine the sound power level of sound sources. This method requires knowledge of two probability distributions. The first is the sampling density, while the second is the prior distribution. In this study, the effect of the prior distribution on the sound power level estimation results was investigated. For this purpose, three prior distributions were used: 1) a normal distribution, 2) a distribution determined using the kernel density estimator, 3) a uniform distribution. The sound power level results determined by the engineering method were used to illustrate the proposed solutions and carry out the analysis. The results of the experiment were compared with the results of the sound power level determined using the precision method in the hemi-anechoic room according to ISO 3745:2012. The statistical inference has been carried out based on results of non-parametric statistical tests at the significance level α = 0.05.

Rozkład a priori w czynniku bayesowskim a wybór modelu klas ukrytych

Kapłon R.

Badania Operacyjne i Decyzje

2009

nr 3

88-94

Na etapie wyboru liczby segmentów w analizie klas ukrytych kryteria informacyjne są często stosowane. Szczególne miejsce zajmuje tutaj kryterium bayesowskie BIC, które można wyprowadzić – dokonując pewnych uproszczeń – z koncepcji czynnika bayesowskiego. W czynniku tym pojawia się rozkład a priori parametrów, którego nie ma w BIC. Z tego względu w pracy podjęto próbę znalezienia takiego rozkładu a priori, aby skuteczność tak powstałego kryterium była większa niż skuteczność BIC.

Estimating the values of parameters in latent class analysis, one needs to know the number of clusters in advance. It is crucial to determine a criterion which enables confirmation of the superiority of one number of classes over the others. A statistical approach, which is based on a likelihood ratio test (LRT), contends with the difficulties of assessing the null distribution of LRT statistics. As a remedy, information criteria like the Bayesian information criterion (BIC) can be used. This criterion is an approximation of a Bayes factor that depends on the prior distribution. Apparently, if one combines BIC and a suitable prior, the effectiveness of such a criterion increases in comparison to the standard BIC. In this article we propose such a prior distribution. In order to do this, a simulation study is carried out and the data collected enable the construction of a nonlinear regression model. The number of classes and the values of the required parameter are chosen as the predictor and the dependent variable, respectively. Such an approach enables the estimation of the values of the parameters a priori given the number of clusters. The performance of the new criterion is better than the Bayesian information criterion by up to 58%.